Designing Distribution Networks with Reverse Flows

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Designing Distribution Networks with Reverse Flows
Vedat Verter, McGill University, Montreal
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Research Collaborators

• Necati Aras, Bogaziçi University, Istanbul
• Rico Wojanowski, Fraunhofer Institute,
  Magdeburg
• Tamer Boyaci, McGill University, Montreal

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The Context
Environmental Sustainability
Waste Reduction
Env. Conscious Manufacturing
Consumption Economy
Product Recovery
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Product Recovery
Product recovery aims at capturing the remaining
economical value in used, unsold, or obsolete
products. Product recovery creates reverse
flows in the distribution network.
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Product Recovery Activities

• collection of used products
• inspection/separation to determine the condition
  of the return.
• reprocessing the return, which may include reuse,
  recycling, remanufacturing or repair.
• disposal of returns which are unrecoverable.
• redistribution of recovered products.

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A Distribution Network with Forward Flows
Plants
Distribution Centers
Customer Zones
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A Network with Forward and Reverse Flows
Customer Zones
Plants
Distribution/Inspection Centers
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A Network with Forward and Reverse Flows
Customer Zones
Plants/ Inspection Centers
Distribution
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The Design Problem
Given a set of existing plants and customer
zones, determine the optimal number and location
of the distribution centers and inspection
centers and remanufacturing facilities so as to
minimize the total operational cost.
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Assumptions

• Assumptions
• There is a single product.
• At each customer zone, a fraction of the local
  demand is returned.
• Unit manufacturing and remanufacturing costs do
  not vary with plant location, and remanufacturing
  is cheaper.

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Parameters (Model 1)
Plants
Distribution/Inspection Centers
Customer Zones
fj
cij
ejk
si , ai
dk , rk
a
cji
hi
gj
ekj
disposals
1-a
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Parameters (Model 1)
fj fixed cost of opening a distribution
center at site j gj fixed cost of opening an
inspection center at site j hi fixed cost of
opening a remanufacturing facility at plant i cij
cost of shipping one unit from plant i to
distribution center j ejk cost of shipping one
unit from inspection center j to customer zone
k cji cost of shipping one unit from
inspection center j to plant i ekj cost of
shipping one unit from customer zone k to
inspection center j dk demand at customer zone
k rk return at customer zone k (rk g dk ) a
proportion of returns found to be
remanufacturable after insp. si manufacturing
capacity of plant i ai remanufacturing
capacity of plant i
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Variables (Model 1)
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MIP Formulation (model 1)
minimize total cost fixed cost transportation
cost s.t. all demand is satisfied all
returns are collected total inflow total
outflow at dist. centers total inflow total
outflow at insp. centers manufacturing
capacity not exceeded remanufacturing capacity
not exceeded all returns are to be
remanufactured
P1
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MIP Formulation (Model 1)
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Lagrangean Relaxation based Solution Method
P1
minimize total cost fixed cost transportation
cost s.t. all demand is satisfied all
returns are collected total inflow total
outflow at dist. centers total inflow total
outflow at insp. centers manufacturing
capacity not exceeded remanufacturing capacity
not exceeded all returns are to be
remanufactured
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Solution Method
Relaxing the two sets of constraints decomposes P
into two sub-problems P1 and P2.
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Solution Method
P
t0 iterations
multipliers
dec. var.
multipliers
dec. var.
P1 and P2 are solved optimally.
Using the distribution/inspection centers opened
in P1 and P2, we can find a feasible solution for
problem P by solving a transshipment problem.
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Two-Level Lagrangean Relaxation
P
t0 iter.
multipliers
dec. var.
multipliers
dec. var.
t2 iter.
t1 iter.
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Computation Time for t040, t1t2100 (sec)
Optimal Solution Problem Set1 Set2 Set3 Set4
Set5 Avg. 5-10-20 29.5 222.7 43.3 9.6 13.8 63.8
5-20-40 1068.5 952.3 1068.3 4977.3 2977.4 2208.7
Two-Level LR Problem Set1 Set2 Set3 Set4 Set5
Avg. 5-10-20 192.6 195.1 167.9 135.8 133.7 165.0
5-20-40 785.2 733.0 804.3 902.5 799.9 804.9
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Parameters (Model 2)
Plants With Inspection Centers
Distribution Centers
Customer Zones
fj
cij
ejk
si , ai
dk , rk
li
cji
disposals
ekj
1-a
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Variables (Model 2)
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MIP Formulation (Model 2)
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Computational Experiments
We consider a problem with 5 plants, 10
alternative sites for distribution/inspection
centers and 20 customer zones. We create 5
instances of this problem by a) randomly
generating five sets of cost and demand
parameters, and then b) setting the following
values to the parameters Capacities si300,
ai200 Fixed costs fj50, gj75, hi100,
and varying li in the range 125-175
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Fixed cost of Remanuf.Inspec. Facility
li125
Return Recovery Model 1 Model 2 Cost advantage
Rate Rate of Model 2 () 0.2 0.2 1089.8 1081
.9 0.73 0.2 0.4 1088.1 1070.5 1.61 0.2 0.6 1083.
6 1055.2 2.62 0.2 0.8 1186.0 1137.9 4.05 0.2 1.0
1197.1 1127.9 5.77 0.4 0.2 1184.0 1218.3 -2.89
0.4 0.4 1281.9 1259.6 1.74 0.4 0.6 1302.0 1246.8
4.24 0.4 0.8 1429.7 1333.4 6.74 0.4 1.0 1446.4
1330.0 8.05
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Fixed cost of Remanuf.Inspec. Facility -
continued
li125
Return Recovery Model 1 Model 2 Cost advantage
Rate Rate of Model 2 () 0.8 0.2 1461.2 1494
.8 -2.29 0.8 0.4 1585.6 1550.9 2.19 0.8 0.6 175
8.4 1718.7 2.25 0.8 0.8 1995.6 1904.3 4.58 0.8 1
.0 - - - 1.0 0.2 1536.9 1599.9 -4.09 1.0 0.4 16
70.2 1660.6 0.58 1.0 0.6 2008.6 2006.9 0.08 1.0
0.8 - - - 1.0 1.0 - - -
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Cost Advantage of Model 2 ()
fj50, gj75, hi100
Return Recovery li125 li150
li175 Rate Rate 0.2 0.2 0.73 -1.54 -3.71 0.2
0.4 1.61 -0.68 -2.89 0.2 0.6 2.62 0.31 -1.95 0
.2 0.8 4.05 -0.16 -4.19 0.2 1.0 5.77 1.62 -2.51
0.4 0.2 -2.89 -4.77 -6.64 0.4 0.4 1.74 -2.10 -5.
70 0.4 0.6 4.24 0.4 -3.32 0.4 0.8 6.74 1.52 -3.6
1 0.4 1.0 8.05 2.94 -2.27
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Cost Advantage of Model 2 () - continued
fj50, gj75, hi100
Return Recovery li125 li150 li175
Rate Rate 0.8 0.2 -2.29 -5.41 -8.37 0.8 0.4 2
.19 -2.48 -6.78 0.8 0.6 2.25 -3.32 -8.36 0.8 0.8
4.58 -1.65 -7.36 0.8 1.0 - - - 1.0 0.2 -4.09 -
6.84 -9.58 1.0 0.4 2.19 -3.77 -7.75 1.0 0.6 0.08
-5.78 -11.0 1.0 0.8 - - - 1.0 1.0 - - -
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Concluding Remarks
We focused on the effect of two uncertain
parameters of a product recovery network design
problem. As the recovery rate increases, opening
the inspection centers at the upstream echelon
along with remanufacturing facilities is a better
design strategy. The extent of scale economies
in building the joint remanufacturing
inspection facility will determine the design
strategy choice.
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Concluding Remarks
Sequential versus Integrated design
approaches The reverse network structure is
usually robust. However the forward network needs
to be re-structured so as to incorporate the
presence of return flows.
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Retail-Collection Network Design under
Deposit-Refund
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Closed-Loop Supply Chains

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Collection Process
Return Product Flow
Collector
Product holder

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Target Recovery/Recycling Rates

• Example WEEE Directive in EU
• refrigerators and washing machines 75
• cathode ray tubes 70
• computer equipment 55

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Policies for Collection Regulation

• Mandatory take-back legislation
• Price-based policies
• taxes on the use of virgin materials
• recycling subsidies
• disposal fees
• deposit-refund requirements

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Regulation of Collection Activity
Return Product Flow
Retailer / Collector
Product holder

Product Flow
Regulator
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Designing a Collection System with Deposit-Refund

• Existing retail network
• Drop off collection strategy
• Continuous model at market level
• Stochastic utility choice model at the individual
  level

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Retail Activity
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Collection Activity
(included in the retail price)
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The Firms Profit Function
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Average Return Density
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Average Sales Density
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An Individuals Decisions

• 
  Return
• Buy
• 
  Do Not Return
• Do Not Buy

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Individuals Utility to Buy
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Individuals Utility to Return
Individuals Utility from not Returning
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Individual Probabilities

• Assume the random variables are uniformly
  distributed.
• Purchase and return if
• Purchase and not return if

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Computational Experiments

• Voluntary deposit-refund
• Government-initiated deposit-refund

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The impact of deposit-refund when it is added on
retail price r0
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The impact of deposit-refund when the firm
optimizes retail price and collection radius
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The impact of return value on voluntary and
maximum deposit refund
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The impact of deposit refund when collection
radius is bounded
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The impact of deposit refund when the firm is
required to offer collection at retail facilities
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Directions for Future Research

• Firms perspective Integrate collection model in
  the design of reverse logistics network.
• Governments perspective Develop a mechanism to
  share the firms profit loss due to
  deposit-refund requirements.
• Governments perspective Analyze the firm-level
  impact of other policy tools to increase recovery
  rate.

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• Questions ?
• Comments ?